Related papers: A construction of Combinatorial NLTS
Neural network quantum states (NQS) have emerged as a powerful and flexible framework for addressing quantum many-body problems. While successful for model Hamiltonians, their application to molecular systems remains challenging for several…
In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
We consider a family of tensor network states defined on regular lattices that come with a natural definition of an adiabatic path to prepare them. This family comprises relevant classes of states, such as injective Matrix Product and…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
Commuting local Hamiltonians provide a testing ground for studying many of the most interesting open questions in quantum information theory, including the quantum PCP conjecture and the existence of area laws. Although they are a…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
We propose a method to construct the ground state $\psi(\lambda)$ of local lattice hamiltonians with the generic form $H_0 + \lambda H_1$, where $\lambda$ is a coupling constant and $H_0$ is a hamiltonian with a non degenerate ground state…
The goal of this work is to define a notion of a quantum neural network to classify data, which exploits the low energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we…
The study of ground state energies of local Hamiltonians has played a fundamental role in quantum complexity theory. In this paper, we take a new direction by introducing the physically motivated notion of "ground state connectivity" of…
We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems…
In this article a study was made of the conditions under which a Hamiltonian which is an element of the complex $ \left\{ h (1) \oplus h(1) \right\} \uplus u(2) $ Lie algebra admits ladder operators which are also elements of this algebra.…
We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…